If (a_n=\frac{n}{n+2}), at which term will (a_n=\frac{5}{7})?
Answer and explanation
Correct answer: (5)th
The general rule gives the value of the term directly when its position is known: \\(a_n=\\frac{n}{n+2}\\). We need to find the position n for which the term equals \\(\\frac{5}{7}\\). Thus, substitute the required value and solve the resulting equation. Since a term number is normally a positive integer, the valid solution must be checked as a whole-number position.
Set \\(\\frac{n}{n+2}=\\frac{5}{7}\\). Cross-multiplication gives \\(7n=5(n+2)\\), so \\(7n=5n+10\\). Subtracting \\(5n\\) from both sides gives \\(2n=10\\), hence \\(n=5\\). Checking gives \\(a_5=\\frac{5}{5+2}=\\frac57\\). Therefore, the fifth term, option D, is correct.
Frequently asked questions
What is the correct answer to this question?
(5)th
Why is this the correct answer?
The general rule gives the value of the term directly when its position is known: \\(a_n=\\frac{n}{n+2}\\). We need to find the position n for which the term equals \\(\\frac{5}{7}\\). Thus, substitute the required value and solve the resulting equation. Since a term number is normally a positive integer, the valid solution must be checked as a whole-number position.
Set \\(\\frac{n}{n+2}=\\frac{5}{7}\\). Cross-multiplication gives \\(7n=5(n+2)\\), so \\(7n=5n+10\\). Subtracting \\(5n\\) from both sides gives \\(2n=10\\), hence \\(n=5\\). Checking gives \\(a_5=\\frac{5}{5+2}=\\frac57\\). Therefore, the fifth term, option D, is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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